Power statistical term

The average uninterruptible power supply (ups)/generator/ utility system has an availability of about 3-nines, explained Thomas Ditoro, the project s electrical engineer. The statistical term availability is industry jargon meaning the fraction of time the system is available for use.8 A system available 99.9 percent of the time is a 3-nines system, a system with 99.9999 percent availability is a 6-nines system, and so forth. The most redundant ups can achieve an availability of 4-nines. The fuel cell system at First National Bank of Omaha has a calculated availability of 6- to 7-nines. ... 

The evaluative and subjective associations made by the consumer must be understood when assessing a product these are measured using market research techniques. If the market is understood, fragrances can be developed to match or enhance the image of a particular product or market segment. Sensory analysis is also an important tool in this process. Using powerful statistical techniques, the odour relationships between different products or perfumes can be characterized and quantified, and the results combined with market research to enable the subjective associations to be interpreted in odour terms. 

There are several ways to reduce both type I and type II errors available to researchers. First, one can select a more powerful statistical method that reduces the error term by blocking, for example. This is usually a major goal for researchers and a primary reason they plan the experimental phase of a study in great detail. Second, as mentioned earlier, a researcher can increase the sample size. An increase in the sample size tends to reduce type II error, when holding type I error constant that is, if the alpha error is set at 0.05, increasing the sample size generally will reduce the rate of beta error. 

Using a principal components analysis (PCA) has become a popular way to study movements of the term structure because it allows one to aggregate the risks in a nonarbitrary way. The concepts behind this powerful statistical technique are fairly straightforward ... 

The amount of information obtainable from any QSAR analysis, and hence ultimately its predictive power, largely depends on the initial design of the underlying experimental study. Only if the compounds included in the test data set are true representatives of the chemical class(es) concerned, can the maximum information be extracted from the data. The members of the training set, which are used to derive the model, should be as diverse as possible with respect to their structural features. In statistical terms this means that they should reveal minimum intercorrelation and maximum variance in the properties regarded relevant for the effects studied. 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

Models should be assessed not only in terms of their goodness of fit (i.e., statistical quality) but also in terms of their predictive power. The predictive power of a model can be assessed only by estimating the activity of a set of compounds not included in the original model. 

The two-point correlation function has been worked out explicitly by Berkolaiko et.al. (2001) and has been shown to coincide with the statistics of so-called Seba billiards, that is, rectangular billiards with a single flux line. The first few terms in a power series expansion of the form factor have been derived by Kottos and Smilansky (1999) and Berkolaiko and Keating (1999) and yield... 

Advanced mathematical and statistical techniques used in analytical chemistry are often referred to under the umbrella term of chemometrics. This is a loose definition, and chemometrics are not readily distinguished from the more rudimentary techniques discussed in the earlier parts of this chapter, except in terms of sophistication. The techniques are applied to the development and assessment of analytical methods as well as to the assessment and interpretation of results. Once the province of the mathematician, the computational powers of the personal computer now make such techniques routinely accessible to analysts. Hence, although it would be inappropriate to consider the detail of the methods in a book at this level, it is nevertheless important to introduce some of the salient features to give an indication of their value. Two important applications in analytical chemistry are in method optimization and pattern recognition of results. 

No attempt will be made here to extend our results beyond the simple lowest-order limiting laws the often ad hoc modifications of these laws to higher concentrations are discussed in many excellent books,8 11 14 but we shall not try to justify them here. As a matter of fact, for equilibrium as well as for nonequilibrium properties, the rigorous extension of the microscopic calculation beyond the first term seems outside the present power of statistical mechanics, because of the rather formidable mathematical difficulties which arise. The main interests of a microscopic theory lie both in the justification qf the assumptions which are involved in the phenomenological approach and in the possibility of extending the mathematical techniques to other problems where a microscopic approach seems necessary in the particular case of the limiting laws, obvious extensions are in the direction of other transport coefficients of electrolytes (viscosity, thermal conductivity, questions involving polyelectrolytes) and of plasma physics, as well as of quantum phenomena where similar effects may be expected (conductivity of metals and semi-... 

The first precise or calculable aspect of experimental design encountered is determining sufficient test and control group sizes to allow one to have an adequate level of confidence in the results of a study (that is, in the ability of the study design with the statistical tests used to detect a true difference, or effect, when it is present). The statistical test contributes a level of power to such a detection. Remember that the power of a statistical test is the probability that a test results in rejection of a hypothesis, H0 say, when some other hypothesis, H, say, is valid. This is termed the power of the test with respect to the (alternative) hypothesis H. ... 

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